Combinatoria de permutaciones

Abstract

Permutations are perhaps one of the most basic and important combinatorial structures. They appear in Mathematics and other fields of Science and Technology under many different appearances, for instance as linear orders, elements of the symmetric group, or associated to certain matrices and graphs. There are also many interesting statistics associated to permutations. Among others, in this work, we explore the number of ascents, the number of inversions and the number of cycles. In connection with theses statistics there are many interesting results and concepts like recurrence formulas, generating functions and a collection of important numbers not only in combinatorics but in some other fields as Eulerian numbers, Stirling numbers of first and second kind, etc. Finally, in the last chapter we present some aplications to run tests based on the length of ascents and descents and also the connection between central and factorial moments.